Continuous Program Search

TL;DR

This work reframes genetic programming with symbolic policies as a continuous search problem by embedding programs into a latent space where small movements have predictable behavioral effects. It introduces GPTL, a typed trading DSL whose four semantic components enable a block-factorized latent representation learned by a transformer-based VAE, and diagnostics to identify a trust region of valid, behavior-local mutations. A geometry-aware mutation operator, including a flow-based direction predictor restricted to paired entry–exit subspaces, is trained on logged evolutionary traces and used as a drop-in replacement for standard mutation under a fixed $( ext{μ+λ})$ ES. Empirically, this approach yields faster discovery and higher median out-of-sample Sharpe across five assets, outperforming isotropic and simple dual-block mutations while preserving the existing evolutionary framework. The findings suggest that aligning mutation structure with latent behavioral geometry substantially improves search efficiency and robustness in continuous program search, with broad applicability beyond trading domains.

Abstract

Genetic Programming yields interpretable programs, but small syntactic mutations can induce large, unpredictable behavioral shifts, degrading locality and sample efficiency. We frame this as an operator-design problem: learn a continuous program space where latent distance has behavioral meaning, then design mutation operators that exploit this structure without changing the evolutionary optimizer. We make locality measurable by tracking action-level divergence under controlled latent perturbations, identifying an empirical trust region for behavior-local continuous variation. Using a compact trading-strategy DSL with four semantic components (long/short entry and exit), we learn a matching block-factorized embedding and compare isotropic Gaussian mutation over the full latent space to geometry-compiled mutation that restricts updates to semantically paired entry--exit subspaces and proposes directions using a learned flow-based model trained on logged mutation outcomes. Under identical $(μ+λ)$ evolution strategies and fixed evaluation budgets across five assets, the learned mutation operator discovers strong strategies using an order of magnitude fewer evaluations and achieves the highest median out-of-sample Sharpe ratio. Although isotropic mutation occasionally attains higher peak performance, geometry-compiled mutation yields faster, more reliable progress, demonstrating that semantically aligned mutation can substantially improve search efficiency without modifying the underlying evolutionary algorithm.

Figures (2)

• Figure 1: Action-sequence divergence between parent and perturbed strategies. Dark colors indicate behavior-local edits. For $\epsilon \leq 0.1$, divergence remains low, defining a trust region. Beyond $\epsilon \geq 0.5$, divergence increases sharply and decoding often fails (gray). This boundary motivates mutation scales in later experiments.
• Figure 2: Signal-level disentanglement under single-block perturbations ($\epsilon=0.3$, per-signal latent dimension = 32). Rows indicate which latent block is perturbed. Columns indicate which program signal changes. Color shows the normalized token edit distance. Perturbations affect only the intended signal, with negligible cross-talk.